Problem: Solve for $q$, $ -\dfrac{9}{5q + 5} = -\dfrac{q - 8}{5q + 5} - \dfrac{7}{q + 1} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5q + 5$ $5q + 5$ and $q + 1$ The common denominator is $5q + 5$ The denominator of the first term is already $5q + 5$ , so we don't need to change it. The denominator of the second term is already $5q + 5$ , so we don't need to change it. To get $5q + 5$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{7}{q + 1} \times \dfrac{5}{5} = -\dfrac{35}{5q + 5} $ This give us: $ -\dfrac{9}{5q + 5} = -\dfrac{q - 8}{5q + 5} - \dfrac{35}{5q + 5} $ If we multiply both sides of the equation by $5q + 5$ , we get: $ -9 = -q + 8 - 35$ $ -9 = -q - 27$ $ 18 = -q $ $ q = -18$